Hecke algebras with independent parameters

Research output: Contribution to journalArticle

Abstract

We study the Hecke algebra (Formula presented.) over an arbitrary field (Formula presented.) of a Coxeter system (W, S) with independent parameters (Formula presented.) for all generators. This algebra always has a spanning set indexed by the Coxeter group W, which is indeed a basis if and only if every pair of generators joined by an odd edge in the Coxeter diagram receives the same parameter. In general, the dimension of (Formula presented.) could be as small as 1. We construct a basis for (Formula presented.) when (W, S) is simply laced. We also characterize when (Formula presented.) is commutative, which happens only if the Coxeter diagram of (W, S) is simply laced and bipartite. In particular, for type A, we obtain a tower of semisimple commutative algebras whose dimensions are the Fibonacci numbers. We show that the representation theory of these algebras has some features in analogy/connection with the representation theory of the symmetric groups and the 0-Hecke algebras.

Original languageEnglish (US)
Pages (from-to)521-551
Number of pages31
JournalJournal of Algebraic Combinatorics
Volume43
Issue number3
DOIs
StatePublished - May 1 2016

Fingerprint

Hecke Algebra
Representation Theory
Diagram
Generator
Algebra
Lame number
Coxeter Group
Commutative Algebra
Semisimple
Symmetric group
Analogy
Odd
If and only if
Arbitrary

Keywords

  • Fibonacci number
  • Grothendieck group
  • Hecke algebra
  • Independent parameters
  • Independent set

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

Cite this

Hecke algebras with independent parameters. / Huang, Jia.

In: Journal of Algebraic Combinatorics, Vol. 43, No. 3, 01.05.2016, p. 521-551.

Research output: Contribution to journalArticle

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